# Alternative theorem, solutions of linear inequalities

Exactly on of the following alternatives holds.

Either the inequality $Ay\ge c \ \ (1)$ has a solution or the $xA=0$, $xc=1 \ \ (2)$ has a nonnegative solution. $A$ is matix of size $m$ x $n$, $x$ an $c$ are vectors of size $m$, $y$ is vector or size $n$.

I have showed that $(1)$ and $(2)$ cannot have solutions simultaneously. How to show if one of them has not solution the other has?

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What do $A, x, y, c$ are? –  Giuseppe Negro Jan 23 '13 at 20:40